Asked by Dan
The function f is defined by f(x)=4x^3+2ax^2+x+b, where a and b are constants.
i) Given that x^2-3x-4 is a factor of f(x), find the value of a and of b.
ii) Hence, factorise f(x) completely.
i) Given that x^2-3x-4 is a factor of f(x), find the value of a and of b.
ii) Hence, factorise f(x) completely.
Answers
Answered by
oobleck
x^2 - 3x - 4 = (x-4)(x+1), so both (x-4) and (x+1) are factors of f(x)
so, f(4) = f(-1) = 0
That means we have
256+32a+4+b = 0
-4+2a-1+b = 0
so a = -53/6 and b = 68/3
f(x) = 4x^3 - 53/3 x^2 + x + 68/3 = (x-4)(x+1)(4x - 17/3)
so, f(4) = f(-1) = 0
That means we have
256+32a+4+b = 0
-4+2a-1+b = 0
so a = -53/6 and b = 68/3
f(x) = 4x^3 - 53/3 x^2 + x + 68/3 = (x-4)(x+1)(4x - 17/3)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.